Discrete age-structured population model with age dependent harvesting and its stability analysis

A discrete age-structured Bernardelli, Lewis and Leslie (BLL) population model for a single species is formulated under age dependent harvesting condition. Here, after an initial period during which the growth of the species is not much, harvesting is performed. Its rate is proportional to the available bio-mass (number of species) of different age group population and decreases with the age of the species. The modified Leslie matrix for the present models is derived. Stability of the system is studied from the ratio of the population densities at different times. As a particular case, not considering the harvesting of species, the classical age-structured population model of [J.N. Kapur, Stability analysis of continuous and discrete population models, Indian J. Pure Appl. Math. 9 (1976) 702–708] is obtained.